I use Thunderbird to send email. My mail server inserts my IP address into the header of my emails. Is there a way to hide this? I’ve thought of sending my mail to the server through Tor but my server apparently refuses tor connections.
Some mail providers, such as Hushmail, strip all IP information from mail before forwarding along. But this is, in general, only a service provided by secure or anonymous email services, not something you can make your existing provider do.
Because the IP addresses in the "Received" headers are stamped on by the mail servers, it's not possible for clients to remove them - you need a complicit mail server working to keep your IP out of the record.
The IP information is added by the mail server. There is nothing you can do to stop this at the client end when sending your email if you are using a reputable mail server. Once upon a time, mail servers were very trusting and often misconfigured and you could get away with things to a greater extent. Thanks to spammers and the risk of mail servers being put into spamming blackholes so that other mail servers will not accept mail from them, things have changed and there is little trust.
You could run your own mail server and have it relay to your ISP server (if your ISP will allow this). This would allow you to fake some of the information and your mail server IP would be in the headers, but your ISP might not inject your client IP address, but this is a fair bit of work and a long shot. Easier just to get a hushmail account!
The only way to reliably achieve what you want is to use a mail service, such as hushmail, which specifically provides a service designed to hide/anonamise sender information.
According to RFC 821 e-mail client should send its domain name in the Helo/EHLO command. So the answer is yes, Thunderbird sends out the IP in e-mail headers.
But this behaviour is reversible, just create mail.smtpserver.default.hello_argument parameter with a example.com string value via Thinderbird's Config Editor (Preferences > Advanced > General). You can assign anything instead of example.com, of course.
Need to be noted, that this is actually will not conceal your IP from mail server, this trick just removes that info from the header. For real anonymity, you should use some kind of anonymization software, such as Tor.